2025-03-05 東京大学生産技術研究所
<関連情報>
ナッシュ流行の理解 Understanding Nash epidemics
Simon K. Schnyder, John J. Molina, Ryoichi Yamamoto, and Matthew S. Turner
Proceedings of the National Academy of Sciences Published:February 27, 2025
DOI:https://doi.org/10.1073/pnas.2409362122
Significance
Social behavior during epidemics is a collective phenomenon: individuals adjust their activity depending on the epidemic state which itself is generated by that same behavior. Game theoretic analysis shows that such dynamics can give rise to a Nash equilibrium. Previously, our analytic understanding of Nash equilibria in epidemics has been extremely limited, leaving us reliant on numerical solutions. Here, we identify an exact analytic expression for fully time-varying Nash equilibrium behavior and resultant disease dynamics. In particular, the strength of social distancing is proven to be proportional to both the perceived infection cost and prevalence. Remarkably, this gives a posteriori justification for the sort of simple heuristics developed to understand diseases like HIV.
Abstract
Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socioeconomic cost. Compartmentalized epidemic models have been extended to include this endogenous decision making: Individuals choose their behavior to optimize a utility function, self-consistently giving rise to population behavior. Here, we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behavior. We leverage an analytic solution that yields fully time-dependent rational population behavior to obtain, 1) a simple relationship between rational social distancing behavior and the current number of infections; 2) scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; 3) characteristic infection costs that divide regimes of strong and weak behavioral response; 4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding of the disease dynamics, useful for both individuals and policymakers. In particular, the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or “bootstrap,” rational behavior.
